Clive Palmer has sent the Chinese embassy in Canberra a letter of apology over his widely criticised comments which he acknowledged were “an insult to Chinese people everywhere”.

The Palmer United party (PUP) leader was criticised by senior figures of both major parties after he referred on live TV to Chinese “mongrels” who “shoot their own people”.

The Chinese embassy initially said Palmer’s “absurd and irresponsible” comments were “full of ignorance and prejudice”. The embassy responded to the apology on Tuesday by saying “any remarks attacking or slandering China would not gain support and were doomed to failure”.

In a letter to the embassy released on Tuesday, Palmer said: “I most sincerely apologise for any insult to Chinese people caused by any of the language I used during my appearance on the ABC television program Q&A.

“I regret any hurt or anguish such comments may have caused any party and I look forward to greater understanding for peace and cooperation in the future.

“We always must have an open mind; an open mind allows us to put ourselves in the other person’s position and brings greater understanding and less conflict to the world. An open mind at least helps me understand why people think the way they do and how we can avoid traps for better understanding. In keeping an open mind, I now come to the realisation that what I said on Q&A was an insult to Chinese people everywhere and I wish to assure them they have my most genuine and sincere apology, that I am sorry that I said the things I said on the program.”

The letter, dated Monday 25 August, included a quote from Mao Zedong. Palmer said it was “in the interest of the whole world that Australia and China have good relations”.

The embassy acknowledged receipt of the letter on Tuesday.

The Chinese ambassador, Ma Zhaoxu, said the Chinese government had “expressed its strong indignation and severe condemnation at Palmer’s insulting remarks” and the Chinese community in Australia had also “strongly protested”.

“The Australian government and people from all walks of life also expressed their strong condemnation and emphasised that Palmer’s insulting remarks on China could by no means represent the Australian government and parliament, let alone its people,” the embassy said in a statement.

“Ambassador Ma stressed that the Chinese people are never to be insulted. Any remarks attacking or slandering China would not gain support and were doomed to failure. The healthy and stable development of China-Australia relations is in the fundamental interests of the two countries and peoples, and cannot be overturned by any individual.”

The Australian Industry Group, which had condemned Palmer’s comments, said the PUP leader’s apology “was a considered and sincere response which should take some heat out of a difficult and potentially damaging situation”.

The group’s chief executive, Innes Willox, said: “The incident serves as a reminder that there should be no room for abuse in political debate and it carries real risks for business if such abuse is directed at our trading partners.”

Palmer made the original comments on Monday last week when asked about allegations he siphoned money from the state-owned Chinese company Citic Pacific, through his Mineralogy company, to his fund his election campaign.

During an exchange on Q&A, Palmer strenuously denied the “false” accusation and accused the Chinese of wanting to take over Australian ports and control Australian resources.

“I don’t mind standing up against the Chinese bastards and stopping them from doing it,” he said. He then called the Chinese “mongrels” and, when the audience reacted, he said: “I’m saying that because they’re communist, because they shoot their own people, they haven’t got a justice system and they want to take over this country.”

Palmer attempted to backtrack the following day, tweeting that his comments were “not intended to refer to Chinese people but to [a] Chinese company which is taking Australian resources and not paying”.

The Chinese-born PUP senator for Western Australian Dio Wang said he did not think his leader’s remark “was a wise comment”.

“I knew where he was coming from but for the greater audience, they don’t understand what it really meant and they felt offended and rightly so,” Wang told Guardian Australia last week.

“The mistake has been made and the damage has been done. I have received a lot of letters from the Chinese communities expressing their concern and anger and I feel for them and I have apologised to every single one of them.”

It is understood a delegation of Chinese community representatives met with Wang at Parliament House on Tuesday.

The PUP senator for Tasmania, Jacqui Lambie, had earlier leapt to her leader’s defence, saying she was concerned about “communist China’s military capacity and threat to Australia”.

“If anybody thinks that we should have a national security and defence policy, which ignores the threat of a Chinese communist invasion – you’re delusional and got rocks in your head,” Lambie said last week.